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Journal of Computer & Robotics 10 (2), 2017 23-35
* Corresponding author. Email: torkaman@pwut.ac.ir
23
A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic Capacitors Effect
Mohammad Reza Yousefi a, Hossein Torkaman b,*
a Department of Electrical, Biomedical and Mechateronics Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
b Faculty of Electrical Engineering, Shahid Beheshti University, A.C., Tehran, Iran
Received 2 June 2017; revised 19 August 2017; accepted 10 September 2017; available online 16 October 2017
Abstract
In this paper, a high frequency contactless power transfer (CPT) system is designed with ∅2 inverter drive. This system
works in 30MHz frequency and 380W power with low voltage stress and considers the inductive link parasitic capacitor
effect. In the design, we formulated the inverter equations first and then suggested another design for the transmitter and the
receiver coils as the energy transfer medium. Following the inverter equations, structures of proper coil are designed for a
CPT system. The results of the coil and ∅2 inverter designs are implemented as a bipolar circuit model which is equal to
considering the inductive link parasitic capacitors. The system characteristics such as the stress, efficiency, mutual induction,
field scattering, magnetic field distribution and the parameters’ variations are evaluated along with analysis. The results
demonstrate that the presented CPT system has high efficiency, low switching voltage stress, small passive energy storage
elements and fast dynamic response.
Keywords: Contactless Power Transfer, High Frequency Inverters, ZVS, ZVDS, ∅2 Inverter Class.
1. Introduction
Contactless power transfer is a young and growing
technology which transfers the energy from a primary side
to a secondary one needless of a wire in which the electro-
magnetic coupling is a method [1]. This method of wireless
energy transmission is highly appropriate for places where
the wire corrosion and the humidity exist. This method is
also applicable in underwater. Contactless energy
transmission has functional merits for static and dynamic
loads like the robots and the electronic vehicles [2, 3]. This
method can be regarded as an effective method for charging
the transportable electronic devices such as mobiles, tablets
and laptops [4-6] in which the CPT systems utilize the
resonance inverters in both the primary and the secondary
sides in order to reach the maximum efficiency [7]. This
issue has caused some troubles in the design and the
construction of such circuits from the sight of the switching
frequency and the out-put power. In other words, an inverter
is limited in the mentioned areas: such as the gate supply, the
output capacitor and the turn-on resistance which have
significant effects on the out-put power and the efficiency.
Even some troubles for PCB designing, passive components
selection, measurement and evaluation analysis will also be
developed.
Research in CPT systems covers an extended number of
subjects such as circuit topologies, magnetic and coil
designs, control and efficiency and system optimization
methods. However, one serious problem that often exists in
H. Torkaman et al. / A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic
Capacitors Effect.
24
most of high power CPT systems is the large passive energy
storage elements due to applications in low frequencies, the
voltage stress on the semi-conductor drivers and the
magnetic cores. In addition, because of working in lower
frequencies, the quality factor of the circuit must be selected
as large which leads to increase the coils’ sizes and also
causes to increase the resistance and the Ohmic losses in the
CPT system. A key solution to solve these problems is to
increase the CPT system working frequencies from the range
of KHz to MHz which leads to eliminate the ferrite core that
leads to decrease the cores’ magnetic losses. The resonance
topologies with higher switching frequencies are often
selected to decrease the switching losses. One structure that
has recently earned some recognition is the E-Class inverter.
The E class inverter is able to perform in higher than 1 MHz
frequencies. Considering its operation in ZVS and ZVDS
conditions, it is able to operate higher power in a specific
voltage. It also benefits from a simpler circuit structure. The
functionality of the E-Class inverter has successfully been
confirmed in recent researches [8-10].
In [11-13], it is shown that in E-Class inverter, the voltage
stress load decreases by putting a resonant tank in series or
in parallel with the load network. By adding a resonant tank
to F-class and F-1-class inverters and combining with E-
class inverter, a combined inverter can be created named EFn
or E/Fn in which “n” index represents the ratio of the
resonance frequency against the switching frequency which
is always an integer number larger or equal to 2. If the index
“n” is even, the inverter is EFn and if odd the inverter is
named as E/Fn. This added resonance network can act as a
resonance tank connected in series or in parallel to the load
network [12, 14-16]. As a result, the out-put power
efficiency and the out-put power capacity are higher than the
ones of E-class inverter in some cases and demonstrate lower
voltage stresses regarding the added parallel resonance tank.
The idea of combining E-Class and F-Class inverters was
first presented in 2002. In this study, the frequency range,
the voltage and the current wave forms were presented in
assorted combinations of the resonance tank.
In [14], the design equations are presented considering
the frequency as the switching frequency and the duty cycle
as 50%. Also in [12], the state space model is presented for
EF inverter of Figure 1. The presented model contains the
ZVS and ZVDS conditions in all duty cycles and all load
quality factor of the added resonance tank.
Fig. 1. The ∅2-Class Inverter
The presented inverter in [13] is also named as ∅2-Class
inverter. The difference in ∅2-Class inverter is in utilizing the
finited input inductance value or L1 instead of an infinited
inductance in EF inverter. The finite inductance of input
choke is that the inductor becomes a part of the load network
and makes the maximum switching frequency to increase,
like E-class inverter which increases the input frequency
from the factor 1 to the factor 4 with the finited input
inductance [17].
The conducted analyses for ∅2 inverters are limited to the
following assumptions: duty cycle is exactly 50% and the
energy capacity or Q, added from the LC resonance network
are high. This issue can practically complicate the
implementation of the resonant LC grid with high Q and few
MHz frequency, especially for power operations. This is
because the equivalent series resistance of the inductor gets
large and leads to increase the losses that can make the EF
and E/F usages limited compared to E-class inverters. In
these inverters, the magnetic cores’ utilizations must also be
avoided since the saturation phenomenon leads to the loss
increase. Therefore, a resonance LC network with low Q and
small inductance must be regarded so as to utilize a single
inductance of a multi-turn air core. ∅2-Class inverter
increases the reflected impedance the secondary to the
primary side in a CPT system, so the power flows in a lower
current stress.
In this paper considering the ∅2-Class inerter advantages
including: the elimination of the second factor harmonic,
decreasing the total THD, increasing the output power
capability, magnetic core elimination and increasing the
reflected resistance, this inverter is utilized as the electronic
drive of the presented CPT system. The structure the CPT is
presented in the frequency of 30 MHz, the power 380 W and
high efficiency. This paper follows the following sections:
In section II, the coil designs for the transmitter and
receiver side will be presented and analyzed. In section III,
a ∅2-Class inverter will be utilized in a CPT system
Journal of Computer & Robotics 10 (2), 2017 23-35
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considering the resulted values in the presented design, and
it will also be analyzed and classified. In section IV,
considering the resulted values of the previous section, the
presented system will be analyzed in the format of an
equivalent circuit as a bi-polar with the parasitic capacitors
of the transmitter and receiver coils. The effect of the
frequency change, the distance and the loading will be
investigated in this model and in the end the significant
results will be concluded and presented in section V.
2. The Flat Coil Design for the CPT System
Considering the position and the location limitations in
the CPT systems, the transmitter coils need to be prioritized
for the designing process. Therefore, in the first step of
designing a CPT system, the coil design will be developed.
In the presented system the flat circular coil is utilized for
the following reasons: (a) The low proximity, skin and DC
losses, (b) The small value of the air gaps flux density.
Two significant and determinative factors in the CPT
system coils design are the quality and the coupling
coefficients which play important roles in the efficiency as
well. The bigger the quality factor, the stronger the coupling
(the magnetic connection) of the coils. However, one should
not always expect that with increasing the quality factor, the
coupling coefficient increases as well especially in the coils
different sizes. On the other hand, increasing the quality
factor, leads to increase the coil’s size which subsequently
ends up having larger Ohmic losses. The size and the
geometry of the transmitter coils are significantly
independent to k and Q indices. Three parameters of Ohmic
resistance, inductance and the capacitance are often
calculable so as to evaluate and design a high frequency flat
coil which is applicable in the contactless power transfer
systems. Generally, two design methods can be presented for
the coils of the contactless power transfer systems. The first
method is based on the coupling in which the coil is designed
considering the voltages and currents of the coil and also the
coupling coefficient. The second method is based on the coil
geometry. In the presented system, in order to improve the
coil operation in the air and accurate calculation of the
parasitic capacitance around the coil, the second method is
implemented.
2.1. Extraction of the Flat Coil Design Equations
As shown in Figure 2 a flat coil from the front view which
is designed for the presented system in the frequency of 30
MHz in which the physical parameters are defined in Table
1. According to the presented definitions in Table 1,
equation (1) can be extracted for this coil.
Table. 1. The symbols characteristics utilized in the coil design
Symbol Description Symbol Description
RDC DC Resistance Do Outer diameter
p Distance between each turns
N Number of turns
a Coil radius c Coil deep radius
w Wire diameter L Wire length
δ Conductivity coefficient
Di Inner diameter of coil space
μ0 Vacuum permeability R Ohmic resistance of coils
f Frequency Rj Receiver radius
M Mutual Inductance Ri Transmitter radius
d Distance between coils
k Coupling coefficient
Fig. 2. The designed flat coil in the frequency of 30 MHz
2 ( )
1( )
4
1. ( )
2
1( )
2
i o
o i
o i
o i
D D N w p
a D D
L N D D
c D D
(1)
According to the aforementioned equations, the values of
the length, the outer diameter, the coil radius and the internal
coil radius can be calculated for a more accurate evaluation
of the flat coil.
iD oD
H. Torkaman et al. / A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic
Capacitors Effect.
26
2.1.1.The Inductance Calculation
One of the most important values for evaluating the
accurate functionality of a CPT system is the precise
calculation of the inductance value of the transmitter and
receiver coil.
2 2
6
( ( ) ) 39.37( )
16 28 ( ) 10o
o
N D w pL H
D N w p
(2)
In this equation, the values are in meters and the
inductance is calculated in Henry. The above equation is not
appropriate for the coils with low turning ratio or the coils in
which the coil pitch is too larger than the wire diameter or if
the ratio 0.2c
a exists.
2.1.2.Calculating the Capacitance Around the Flat Coil
Since the formed parasitic capacitance in the proximity of
a flat coil that is utilized in CPT systems in high frequencies
has a significant numerical value, calculating this value has
a great importance so as to determine the external
capacitance added for the resonance.
The formed capacitance in the coil proximity is a function
of the conductor conductivity coefficient, the diameter of
each turn of the coil, the total number of the turns and the
coil pitch. By increasing the number of the turns, the value
of the formed capacitance in the coil proximity increases
significantly and non-linearly. The value of the proximity
capacitance is often within PF scale and calculable from
equation (3).
2
1( )
(2 )C F
f L (3)
In some applications the value of the coil proximity
capacitance can be used instead of the added capacitance in
the resonance tank.
2.1.3.Resistance
There are losses in two regions of a flat coil: the
conduction losses and the losses of radiation losses. Since
the wavelength is often much longer compared to the coil
(almost 22 meters at 13 MHz frequency), the radiation losses
are disregarded. The conduction loss is a function of the skin
effect and the proximity, however, in the flat coil used in the
presented CPT system, the factor that makes changes to the
coil resistance value is the coil pitch “p”. This has a reverse
relationship with the Ohmic value of the resistance because
of the proximity effect and this effect is non-linear. The
Ohmic value of the resistance can be calculated from the
Kaiser’s high frequency model.
04 ( ( )
4o
dc
N D N w pwR R
w
(4)
2
1( )
( )2
dcRw
(5)
0
1
f
(6)
In which σ the Copper’s conductivity coefficient and
equals 59.6 * 106.
2.1.4.The Quality Factor
Since the series resonance is utilized in the presented
system, the quality factor can be defined as the equation (7).
1 LQ
R C (7)
Using the extracted equations (2)-(6) defined in the
previous sections and replacing them in equation (7), the
quality factor of the flat coil is defined as the equation (8).
60
( ( )39.37.
8 14 ( )10o
o
wN D N w pfQ
D N w p
(8)
From which designing a coil with a high value of Q is
possible and ensure resonance at the desired operating
frequency.
2.1.5.Coupling Coefficient and the Mutual Inductance
The amount of the generated flux by the transmitter which
passes through the receiver determines the coupling
coefficient. In CPT systems, the coupling coefficient is used
instead of the mutual induction for the simplicity. The
coupling coefficient is a function of the geometric shape of
the coil, the distance between coil, and the coils’ direction
toward one another. Assuming the coil angles as zero, the
mutual inductance of the transmitter and the receiver coils
can be calculated from the equation (9).
Journal of Computer & Robotics 10 (2), 2017 23-35
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0 2 2 21 1 0
Cos
2 Cos
TX RXN N
i JI J
i j i j
dM R R
R R d R R
(9)
In which the coupling coefficient is defined as follows
[18-21].
i j
MK
L L
(10)
2.2. Review of the Flat Coil Design in the Presented System
According to the previous sections, the design process of
the flat coil can be explained as follows. Firstly, the
maximum allowed size should be determined since the size
of the receiver coil is of importance regarding the considered
application. Then a size range must be defined for the
transmitter coil. In the following, the maximum Q must be
determined for the transmitter and the receiver and finally,
an appropriate geometry (one of the different kinds of the
flat coils like square, polygon and circular) must be regarded
for the transmitter and the receiver in order to reach the best
possible efficiency in the coil design. The design result of
this section is as follows:
According to equation (9), one can come to conclude
that the maximum coupling coefficient is reached for
two same size coils; as a result, two same size coils
are implemented so as to reach the maximum
coupling coefficient in the presented system.
Fig. 3. The designed flat coils for the frequency of 30 MHz
As stated in the previous section, the resistance value
of the skin effect increases non-linearly. So for
creating a small resistance, large values for Q must
be utilized. Therefore, it is better for the designed
coils to not get too compact. On the other hand,
selecting a large value of the quality factor leads to
increase the inductance and subsequently increases
the length of the conductor and hence the Ohmic
resistance. In the presented system, the large value of
the quality factor is compensated by applying the
frequency of 30 MHz, so the quality factor is selected
as 12 so that ether the skin effect is decreased and the
desired quality factor gets resulted.
When designing a flat coil, the calculation resonance
frequency is of great significance. One appropriate
solution to find the resonance frequency is the study
of the coil impedance. The impedance variations that
includes the resistance and the reactance changes,
versus the frequency variations is illustrated in the
Figure 4. Since this flat coil is a magnetic resonance,
it is witnessed that a Lorentz shape reactance in the
frequency band of 28 to 31 MHz is resulted which has
already been expected. The reactance variation range
is variable until 1000 Ohm, compatible to the resulted
resonance frequency.
Fig. 4. The Frequency-impedance variations
According the calculations in section III, the
inductance value of the primary coil is derived as 7.4
μH. According to this value, a flat circular coil (the
flat circular coils have better flux density compared
to the other types) is considered for the presented
system which has the dimensions of outer diameter
Frequency (MHz)
Impe
dan
ce (
Ω)
-500
0
500
1000
27 28 29 30 31 32
Reactance Resistance
H. Torkaman et al. / A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic
Capacitors Effect.
28
D0=15 cm, inner diameter Di=5 cm, number of turns
6.5 and the conductor diameter of 18 AWG.
3. Design and Modelling of the CPT Transmitter and
Receiver Circuits
The current, in the primary coil of an inductive link has
to be alternating in order to generate an alternating magnetic
field to induce a voltage in the secondary coil. In this regard,
a DC to AC inverter is needed. In order to present higher
efficiencies, the inductive links need large amounts of
energy because of the possibility of the changing distances.
Only specific classes of switching inverters can fulfil such
conditions. As expressed in section I, a ∅2-Class Inverter can
operate in high frequencies. Considering the second
harmony elimination in this inverter, it demonstrates a low
voltage stress which has made it to operate in high levels of
voltage and power. Considering the merits of this inverter,
∅2-Class Inverter is used as a driver of the transmitter circuit.
3.1. The Design of ∅2-Class Inverter in the Presented CPT System
According to Figure 1, the circuit diagram of ∅2-Class
Inverter, L2 and C2 are the inductance and the capacitor of
the resonance tank respectively which are added to decrease
the switching voltage stress. They are adjusted in twice the
switching frequency. The output network inductor L3 and the
capacitor C3 are adjusted. They are adjustable with the
switching frequency so as to create ZVS and ZVDS
conditions. C1 is the switch parallel capacitor, L1 is the finite
input inductance. ∅2-Class Inverter is the improved form of
E-class inverter. So the existing equations of designing E-
class inverters can also be utilized to design ∅2-Class
inverter. Note that the equations 11-13 which are mentioned
in [22] are used to calculate L1, L2 and C2. Since the second
harmonic is the largest harmonic of the system, these values
are designed in twice the value of the switching frequency
so as to eliminate this harmonic and decrease the switch
voltage stress.
1 2 2
1
9 f
Lf C
(11)
2 2 2
1
15 f
Lf C
(12)
2
15
16fC C (13)
In specific applications, ∅2-Class Inverter can be
designed and utilized in “n” times the switching frequency
in order to eliminate the third harmonic or higher [23]. As it
is depicted in Figure 5, according to the developed designs
for ∅2-Class Inverters, the switch voltage stress values of ∅2-
Class inverter compared to E-class inverter have decreased
for as much as 1 KΩ and 200V respectively in the same
amounts of the load.
Fig. 5. The switching voltage stress of E-class inverter compared to ∅2-class inverter
Fig. 6. The current ILMR of ∅2-class inverter
As it is observed in Figure 5, the stress voltage of ∅2
switch inverter is almost 460V which has decreased as 17%
compared to E-class inverter because of eliminating the
second harmonic by the resonant tank which is parallel to the
switch. This voltage decrease is equal to 90V. In the
presented application, the decrease of the switch stress
voltage leads to increase the output power capacity of ∅2-
Class inverter from 0.09 to 0.13 compared to E-class
inverter. Regarding the capacity change, the duty cycle also
has changed from 50% to 37%. Figure 6 illustrates and
compares the duty cycles of ∅2-Class and E-class inverters
in the same load values.
ωt
Class ∅2
Class E
DS
(v)
V
ωt 0 Π 2Π
-2.7
0
2.7
2 (A
)I
Journal of Computer & Robotics 10 (2), 2017 23-35
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Fig. 7. The applied gate voltages of E-class and ∅2-Class inverters
in 50% and 37% duty cycles
Employing ∅2-Class inverter in CPT system has the
following advantages:
Because of the low voltage stresses, inexpensive
switches can be employed for the similar applications
compared to E-class inverters. In high powers, this
cost difference is more touchable and the semi-
conductors benefit from longer mechanical age.
The output power capacity, the maximum operation
frequency and the efficiency of this inverter are
higher compared to the similar topologies, E-Class
and D-Cass inverters. Also, compared to these two
classes, this inverter has higher input voltage which
leads to ripple and input dc current decrease which
subsequently the non-capacitive parasite effect of
Mosfet decreases.
The optimum duty cycle in this class of inverter can
be between 37% and 40% while in the similar system
of E-class has the optimum value of 50%.
Because of operating in high frequencies and small
quality factor of this system, air-core inductors are
employed. Therefore, because of eliminating
magnetic losses of the core, this inverter has higher
efficiency compared to D-Class and E-Class
inverters.
3.2. The system of the Presented CPT with ∅2-Class Drive
In the presented CPT system of Figure 8, ∅2-Class
inverter is employed which has been designed in section 3.1
as the driver of the transmitter circuit. The L3 value of
inductance is going to be employed in two roles as the
primary coil and the resonance inductor. As it was expressed
in section 2.2, for flat coils, the maximum coupling
coefficient happens for two same size coils, therefore, in the
presented structure, the receiver coil is selected in same
inductance value and geometry similar to the ones of L3. The
capacitor Cs is designed and calculated, parallel to the
secondary coil, considering the load value.
Creating the resonance condition by capacitor Cs, the
reactance of the secondary circuit can be eliminated through
which some features will be followed:
Causes the reflected impedance to increase, i.e. the
distance between the transmitter and the receiver gets
decreased
The impedance of the secondary coil gets decreased
and subsequently, the power loss decreases.
The circuit capability of power transmission
increases compared to the non-resonant mode.
The presented system of Figure 8 features the input
voltage of 200V in 30 MHz frequency with the ability of
providing output power of 380V to the load.
Fig. 8. The presented CPT system
The frequency range of the designed inverter in section
3.1 is measured and illustrated in Figure 9 in which the
resulted THD is equal to 3.95%. By re-measuring the THD
value, this time in the receiver circuit of the CPT system
presented in Figure 8, it is observed that the value of THD
changes to 14.2% by changing the distance of the transmitter
and the receiver to 5 cm.
As it is observed in Figure 9, the second harmonic is
eliminated which is the largest harmonic of the presented
CPT. This elimination has led to decrease the voltage stress
in an equal transmission distance compared to E-class
inverter.
(v)
GS
V
0 2Π
5
Class ∅2
Class E
2.5
ωt 0
Π
H. Torkaman et al. / A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic
Capacitors Effect.
30
Fig. 9. The frequency range according to the harmonic hierarchy in the presented system
4. The Equivalent Circuit of the Presented System and
the Parasitic Capacitance
In order to analyze the operation of the presented system
of Figure 8 in various frequency and coupling coefficient
values and also investigate the loading effect on the circuit
operation and the reflected impedance, the equivalent circuit
of the inductive link can be extracted, considering the
resulted numerical design values of Table 2. This equivalent
circuit of the inductive link includes the transmitter and
receiver of the presented model along with the parasitic
capacitance. Figure 10 shows the resulted equivalent circuit.
The capacitors CT and CR contain the transmitter and
receiver resonance capacitors, respectively. CST and CSR
represent the parasitic capacitance of the transmitter and
receiver circuits in the inductive link region and the total
equivalent capacitance is equal to CRE=CSR+CR.
RT
LT
CST
CT
RR
LR
CSR CR RLM.Vin .
Transmitter Receiver
Fig. 10. The SP model of the CPT system along with parasitic capacitance
In order to evaluate the presented model, the efficiency
needs to be calculated in the transmitter and receiver circuits.
In this regard, by applying KVL in the transmitter and the
receiver circuit, the equation (14) and (15) are resulted.
( ) 0Tin LT T T R
T
IV I R j L j MI
j C
(14)
( ) 0T LTLT T T R
ST
I II R j L j MI
j C
(15)
Similarly, by applying KVL in the receiver circuit and
after simplifications and insertion of CSR+CR=CRE, the
equation (16) will be resulted.
01
LLT R R r
RE L
Rj MI I j L R
j C R
(16)
After simplification of the receiver circuit impedance, it
can be divided into two real and imaginary parts.
2 2 2
2 2 21r L r RE L
rec
RE L
R R R C RR
C R
(17)
2 3 2 2
2 2 21R RE L R RE L
rec
RE L
L C R L C RX
C R
(18)
So the impedance of the transmitter circuit can be
obtained from equation (19).
2
( )1
1 ( )
r ref R
tran
T T ref ST R ST
R R j LZ
j C R R j C L C
(19)
By replacing the equation (16) in equation (14), the
reflected impedance can be obtained from equation (20).
2 2 2 2 2
2 2 2
2 2 2 3 2 2
2 2 2
( )
( ) ( )
( )
( ) ( )
r RE L r Lref
r RE L r L r r RE L
RE L R RE L R
r RE L r L r r RE L
M R C R R RZ
L C R R R L R C R
M C R L C R Lj
L C R R R L R C R
(20)
For further simplifications the real and imaginary parts of
the reflected impedance can be separated.
2 2 2 2 2
2 2 2
( )
( ) ( )r RE L r L
ref
r RE L r L r r RE L
M R C R R RR
L C R R R L R C R
(21)
2 2 2 3 2 2
2 2 2
( )
( ) ( )RE L R RE L R
ref
r RE L r L r r RE L
M C R L C R LX
L C R R R L R C R
(22)
Since the imaginary part of the reflected impedance is
equal to zero because of the resonance, Xref=0, the real part
of the reflected impedance should be regarded in the final
equivalent circuit. The final equivalent circuit is extracted as
Figure 11.
Harmonic removed
Mag
(%
of
fund
amen
tal)
Harmonic order
Fundamental
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Fig. 11. The equivalent circuit of the CPT system along with the parasitic capacitance and reflected impedance.
The imaginary part of the equivalent circuit is eliminated
because of the resonance. Therefore, the values of CT and CR
is resulted by resetting the imaginary part to zero.
2 2 2 2 4 2 20 0 0
2 2 2 4 2 20 0 0
2 ( ) 1
( )
T ST ST T ref T ST
T
ST T ef T ST T
L C C R R L CC
C R Rr L C L
(23)
2 20
20
4
2
L L R
R
R L
R R LC
L R
(24)
The efficiency of the transmitter and the receiver is
calculated as below:
(%) 100 %recT
T rec
R
R R
(25)
2 2 20
(%) 100 %LR
r L R RE L
R
R R R C R
(26)
The total efficiency is resulted from multiplying the
transmitter efficiency by the receiver one. As a result, since the
transmitter efficiency is equal to the proportion of the receiver’s
given power to the transmitter’s one, and the receiver’s
efficiency is equal to the proportion of the load’s given power
to the total power of the receiver, the total efficiency of the
entire system is resulted from the equation (27).
2
2
22
2
2
(%) 100 %
( )( )
( )
( ) ( )
L
T
R R r r RE LR r RE L
RE L R
r L R RE L R r
R
M R
R M
L L R R C RL R C R
C R L
R R L C R L RL
(27)
4.1. The Results and Analysis of the Presented Model
According to the fabricated model in the previous section,
the results of this modelling is in the following subsections:
4.1.1.The Effect of the Frequency on the Power and the Output Efficiency
According to equation (27), the efficiency of the
presented system is calculated in various operating
frequencies. The results are illustrated in Figure 12. In this
figure, the resonance capacitor which is suitable for the coils
is calculated with regarding the parasitic capacitance of the
inductive link in each stage in the distance of 5 centimetres.
It is observed that within the range of 30 MHz frequency, the
efficiency is fixed and equal to 95%. So this frequency can
be regarded as appropriate operating frequency for this
application which makes the passive elements of the system
to shrink.
Fig. 12. The efficiency versus the operating frequency
Also by obtaining the value of IR from the equation (16)
and calculating the load voltage, the given power to the load
can be calculated from the equations 28 and 29 by applying
KVL in the receiver circuit.
2L
L R
RE L
RV I
j C R
(28)
2L
L
L
VP
R (29)
Frequency (MHz)
Eff
icie
ncy
(%)
0.2
0.8
0.6
0.4
1
0 5 10 15 20 25 30 35
H. Torkaman et al. / A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic
Capacitors Effect.
32
Fig. 13. The frequency variations versus the given power to the load
According to diagram 13 it is observed that the given
power to the load increases as the frequency increases until
30 MHz which is the desired operating frequency. Then, as
the frequency increases, the given power to the load
decreases. As it is observed, the maximum power of 380W
is reached for the presented system in the frequency of 30
MHz.
4.1.2.The Loading Effect and Distance Change on the Reflected Resistance
Figure 14 shows the load change effect and the frequency
on the reflected resistance in various resonance frequencies.
It is observed that constantly, Xref=0 and Zref=Rref because of
the resonance. The resistance seen from the primary side in
the frequency of 30 MHz and in the load of 1.5 KΩ has the
value of 20Ω which shows the appropriate operating point
and the maximum reflected resistance.
Fig. 14. The frequency and load influences on the reflected resistance
The larger the primary side of the circuit sees the
resistance of the secondary side, the larger efficiency is
transferred. According to diagram 14, it can be interpreted
that the high frequencies are appropriate for large loads. In
the presented model, since a parallel capacitor is used in the
receiver circuit for the resonance creation, it is observed that
by shortening the distance, the observed resistance by the
primary side increases. One of the problems that leads to
huge energy loss in long distances is the equivalent
resistances of the transmitter and the receiver coils and the
passive elements of the circuit which make the CPT systems
limited.
Table. 2. The Values Of ∅2-Class Parameters and Inductive Link at 30 MHZ
With considering maximum switching frequency
With considering E-class inverter Parameters
35.3 µH 625.4 nH L1
1.18 µH 375.26nH L2
5.95 pf 18.75 pf C2
18.6 pf 16.04 pf C1
9.33 pf 20 pf Cp
4.87 pf 4 pf C3
6.95 µH 7.4 µH Lp
6.95 µH 7.4 µH Ls
4.69 nf 13.5pf Cs
100-1kΩ 100-1kΩ RL
200-329 v 200 v Vin
380 380 Po
37.5% 37.5% Duty cycle
2.33-3.86 µH 2.33-3.86 µH M
0-5 cm 0-5 cm Distance
One recommended method that is applicable for longer
distances is the utilization of the parallel capacitor in the
secondary side, because it leads to a decreased current and
subsequently a decreased power loss in ESR (Equivalent
Series Resistance) resistances. Therefore, it can be stated
that if the load value is very smaller than the secondary
reactance, it is better to use series capacitor in the receiver
circuit. If the load value is significantly larger than the
secondary reactance it is better to use the parallel resonance.
Figure 15 shows the distance effect from 1 to 10 cm and
the loading effect on the reflected resistance. It will be
observed that in the load value of 1.5 KΩ the reflected
resistance value is equal to 18Ω. So the appropriate load
value for this application can be selected as 1.5 KΩ. By
increasing the distance from 1 to 10 cm and decreasing the
load from the amount of 1.5 KΩ, the observed resistance
from the primary circuit has got less than 18Ω which
decreases to 2 Ω in the distance of 10 cm from the reflected
resistance.
Frequency (MHz)
Po
wer
Del
iver
ed T
o L
oad
(W
)
20 30 40 50 0
50
100
200
300
380
25 35 45
Ref
lect
ed
Res
ista
nce
(Ω)
500 1000 1500
2000 2500
0 20
30 35
0
5
10
15
20
25
Frequency (MHz) RLoad (Ω)
Journal of Computer & Robotics 10 (2), 2017 23-35
33
Fig. 15. The influence of the Distance and the load value on the reflected resistance
4.1.3.The Effect of Distance and Frequency Change on the Magnetic Connection of the Coils
According to Figure 10, since the resulted equivalent
circuit can also be modeled as a bi-polar (one port represents
the input that is fed by the source and the other side
represents the output which feeding the load), the power
transmission scattering can be calculated by measuring the
linear magnitude scattering parameters (|S21|). This is an
important parameter for analysis a vector network at high
frequencies. S21 is defined as follows:
1
221 2 ( )load source
source load
V RS
V R (30)
The difference of using equation (30) and other similar
parameters like Y parameters, Z parameters, H parameters,
T parameters and ABCD parameters is that the above
parameter employs the matched loads instead of using the
open circuit and short circuit conditions for specifying the
circuit features. This type of description in high frequencies
is way simpler than the open circuit and short circuit
conditions.
Figures 16 and 17 illustrate the S21 value change in the
frequency of 30 MHz. It is observed that the coupling
between the two coils, increases from 0.2 to 0.8 linearly by
the distance reduction from 0.4 to 0.2 in the frequency of 30
MHz. this trend is approximately equal to 1/d3 (d: the
distance between the two coils). Therefore the system
efficiency increases through the distance reduction to an
extent in which it reaches the critical point when S21 is equal
to 0.95. When the magnetic coupling of two coils exceeds
the value of 0.95, the system remains in its peak of
efficiency. In this point, the frequency separation is obvious
in the distance of 0.2 cm. In the frequency splitting part, the
coupling of the two coils gets weaker until when the two
separated parts get convergent again in the frequency of f=30
MHz. This point can also be named as the critical coupling
point which represents the longest distance in which the
maximum efficiency is still available. Figure 16 actually
shows a parametric study of the system “S” as a function of
the transfer distance.
Fig. 16. The S21 as a function of the frequency and the distance
Fig. 17. S21 variations versus the frequency
The results of the models’ simulation shows that in
frequencies less or higher than 30 MHz the coupling value
between the two coils gets decreased. Figure 17 has also
shown the S value analysis. As it is observed, the system
efficiency changes rapidly by the frequency and coupling
variations between the transmitter and the receiver. The peak
efficiency is in the frequency of 30 MHz when the system is
Frequency (MHz)
Mag
nit
ud
e (S
21)
36
26
32 30 28 34 0.4
0.3 0.2
0.2
0.4
0.6
0.8
Dis
tan
ce (
cm)
18 14 10
6 2
10
1
5
2
4
0 RLoad (kΩ)
Reflected resistance (Ω)
Frequency (MHz)
)21
Mag
nitu
de (
S
27 28 29 30 31 32
0.1
0.5
0.3
0.7
Abs(S21)
H. Torkaman et al. / A New System of Contactless Power Transfer with Low Voltage Stress and Parasitic
Capacitors Effect.
34
in the resonance mode and the two coils have a strong
magnetic coupling (S21) of 0.7. The fields around a high
frequency transmitter are called the near-field which are far
or near to the emitting source in which the standard of the
remoteness and the nearness is the wavelength of the emitted
waves. According to the S21 parameter, since a flat designed
coil is a magnetic resonator, the dominant field component
of this coil is the magnetic field. If the near-field effect is
plot, a strong local field in the distances of 0 to 15 cm will
be observed in this circular flat coil.
Fig. 18. The magnetic field distribution in the flat designed coil
The following considerations are taken into account of
the design procedure:
In order to design and analyze the presented system,
the frequency of 30 MHz is utilized since this
frequency is desirable for designing small volume
CPT systems. Also it is a definite and desirable
frequency for analyzing the broadband and drawing
the points in the space for near-field systems.
It was shown that if there is no limitations for the coil
designs, the maximum efficiency happens for the two
same size coils. Therefore, in the presented system,
the two same size coils are employed in the circuits
of the transmitter and the receiver. However, if there
are coil design limitations, according to equation 31
an appropriate coil can be designed.
2 2
1 1
V LK
V L (31)
One of the most important parameters for high
frequency inductors is the value of their stray
capacitor, since the presented system has been
designed based on the electromagnetic coupling. If
the value of these stray capacitors is not calculated,
an undesired resonance in the transferred efficiency
may be resulted. Therefore, the effect of the formed
capacitors around the inductive link is calculated and
employed in the design and analysis.
A ∅2-Class inverter whose parameters are extracted
based on the E-class inverter design equations is
designed in the frequency of 30 MHz in which the
THD is suitable and equal to 3.85%. In the following,
this designed inverter is utilized in a CPT system with
the frequency of 30 MHz and the model of its
inductive link is analyzed and investigated. It is
shown that the presented system demonstrates the
efficiency of 95%.
According to the frequency range of the presented
system, it can be concluded that ∅2-Class inverter
does not present the second harmonic, thus
demonstrates lower THD against an E-Class inverter.
In the following, according to the results, the switch
voltage stresses will be lower and. ∅2-Class inverters
will also have better adjustability EMI compared to
E-class inverters.
5. Conclusion
This paper deals with the investigation and the design of
a CPT system which works upon a ∅2-class inverter. An
analysis has been presented based on the coil design in the
contactless system. According to this design, a coil with the
appropriate dimensions and geometry for a CPT system can
be presented. The optimum values for the ∅2-class inverter
were extracted from the numerical design of an E-class
inverter. The constructed inverter in the CPT structure was
operated and it was shown that the voltage stress has
decreased to 17% compared to E-class inverter. Therefore,
the presented system has a higher power output capacity. In
the following, a bipolar equivalent circuit was presented for
the presented structure in which the CPT system was
analyzed magnetically and from the point of the frequency.
The analysis of the presented circuit has shown that in the
frequency of 30 MHz the efficiency is 95% with the THD
index is 3.85% along with the maximum efficiency, power
and coupling.
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Hei
ght
(cm
)
0.2
-0.2
0 Length (cm)
Journal of Computer & Robotics 10 (2), 2017 23-35
35
References
[1] Zhou, W.; Jin, K., "Efficiency Evaluation of Laser Diode in Different Driving Modes for Wireless Power Transmission", IEEE Transactions on Power Electronics, vol. 30, no. 11, pp. 6237-6244 (2015).
[2] Sato, F.; Murakami, J.; Suzuki, T.; Matsuki, H.; Kikuchi, S.; Harakawa, K.; Osada, H.; Seki, K., "Contactless energy transmission to mobile loads by CLPS-test driving of an EV with starter batteries", IEEE Transactions on Magnetics, vol. 33, no. 5, pp. 4203-4205 (1997).
[3] Covic, G. A.; Boys, J. T.; Kissin, M. L. G.; Lu, H. G., "A Three-Phase Inductive Power Transfer System for Roadway-Powered Vehicles", IEEE Transactions on Industrial Electronics, vol. 54, no. 6, pp. 3370-3378 (2007).
[4] Liu, X.; Hui, S. Y., "Simulation Study and Experimental Verification of a Universal Contactless Battery Charging Platform With Localized Charging Features", IEEE Transactions on Power Electronics, vol. 22, no. 6, pp. 2202-2210 (2007).
[5] Liu, X.; Hui, S. Y., "Optimal Design of a Hybrid Coil Structure for Planar Contactless Battery Charging Platform", IEEE Transactions on Power Electronics, vol. 23, no. 1, pp. 455-463 (2008).
[6] Achterberg, J.; Lomonova, E. A.; Boeij, J. d., "Coil Array Structures Compared for Contactless Battery Charging Platform", IEEE Transactions on Magnetics, vol. 44, no. 5, pp. 617-622 (2008).
[7] Covic, G. A.; Elliott, G.; Stielau,O. H.; Green, R. M.; Boys, J. T., "The design of a contact-less energy transfer system for a people mover system", in International Conference on Power System Technology, pp. 79-84 (2000).
[8] Sokal, N. O.; Sokal, A. D., "Class E-A new class of high-efficiency tuned single-ended switching power amplifiers", IEEE Journal of Solid-State Circuits, vol. 10, no. 3, pp. 168-176 (1975).
[9] Aldhaher, S.; Luk, P. C. K.; Whidborne, J. F., "Wireless power transfer using Class E inverter with saturable DC-feed inductor", in IEEE Energy Conversion Congress and Exposition, pp. 1902-1909 (2013).
[10] Aldhaher, S.; Luk, P. C. K.; Whidborne, J. F., "Tuning Class E Inverters Applied in Inductive Links Using Saturable Reactors", IEEE Transactions on Power Electronics, vol. 29, no. 6, pp. 2969-2978 (2014).
[11] Mediano, A.; Sokal,N. O., "A Class-E RF power amplifier with a flattop transistor-voltage waveform", IEEE Transactions on Power Electronics, vol. 28, no. 11, pp. 5215-5221 (2013).
[12] Kaczmarczyk, Z., "High-efficiency Class E, EF2, and E/F3 inverters", IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1584-1593 (2006).
[13] Kee, S. D.; Aoki, I.; Hajimiri, A.; Rutledge, D., "The class-E/F family of ZVS switching amplifiers", IEEE Transactions on Microwave Theory and Techniques, vol. 51, no. 6, pp. 1677-1690 (2003).
[14] Grebennikov, A., "High-Efficiency Class E/F Lumped and Transmission-Line Power Amplifiers", IEEE Transactions on Microwave Theory and Techniques, vol. 59, no. 6, pp. 1579-1588 (2011).
[15] Hayati, M.; Sheikhi, A.; Grebennikov, A., "Effect of nonlinearity of parasitic capacitance on analysis and design of Class E/F3 power amplifier", IEEE Transactions on Power Electronics, vol. 30, no. 8, pp. 4404-4411 (2015).
[16] Rivas, J. M.; Han, Y.; Leitermann, O.; Sagneri, A. D.; Perreault, D. J., "A High-Frequency Resonant Inverter Topology With Low-Voltage Stress", IEEE Transactions on Power Electronics, vol. 23, no. 4, pp. 1759-1771 (2008).
[17] Green, A. W.; Boys, J. T.,"10 kHz inductively coupled power transfer-concept and control", in Fifth International Conference on Power Electronics and Variable-Speed Drives, pp. 694-699 (1994).
[18] Fotopoulou, K.; Flynn, B. W., "Wireless Power Transfer in Loosely Coupled Links: Coil Misalignment Model", IEEE Transactions on Magnetics, vol. 47, no. 2, pp. 416-430 (2011).
[19] Ho, S. L.; Wang, J.; Fu, W. N.; Sun, M., "A Comparative Study Between Novel Witricity and Traditional Inductive Magnetic Coupling in Wireless Charging", IEEE Transactions on Magnetics, vol. 47, no. 5, pp. 1522-1525 (2011).
[20] Mizuno, T.; Yachi, S.; Kamiya, A.; Yamamoto, D., "Improvement in Efficiency of Wireless Power Transfer of Magnetic Resonant Coupling Using Magnetoplated Wire", IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 4445-4448 (2011).
[21] Zhang, F.; Hackworth, S. A.; Fu, W.; Li, C.; Mao, Z.; Sun, M., "Relay Effect of Wireless Power Transfer Using Strongly Coupled Magnetic Resonances", IEEE Transactions on Magnetics, vol. 47, no. 5, pp. 1478-1481 (2011).
[22] Madsen, M.; Knott, A.; Andersen, M. A. E., "Low Power Very High Frequency Switch-Mode Power Supply With 50 V Input and 5 V Output", IEEE Transactions on Power Electronics, vol. 29, no. 12, pp. 6569-6580 (2014).
[23] Aldhaher, S.; Yates, D. C.; Mitcheson, P. D., "Modeling and Analysis of Class EF and Class E/F Inverters with Series-Tuned Resonant Networks", IEEE Transactions on Power Electronics, vol. 31, no. 5, pp. 3415-3430 (2016).